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Chern forms of singular metrics on vector bundles

Journal article
Authors Richard Lärkäng
Hossein Raufi
Jean Ruppenthal
Martin Sera
Published in Advances in Mathematics
Volume 326
Pages 465-489
ISSN 0001-8708
Publication year 2018
Published at Department of Mathematical Sciences, Algebra and Geometry
Pages 465-489
Language en
Links https://doi.org/10.1016/j.aim.2017....
Subject categories Mathematical Analysis, Geometry

Abstract

We study singular hermitian metrics on holomorphic vector bundles, following Berndtsson–Păun. Previous work by Raufi has shown that for such metrics, it is in general not possible to define the curvature as a current with measure coefficients. In this paper we show that despite this, under appropriate codimension restrictions on the singular set of the metric, it is still possible to define Chern forms as closed currents of order 0 with locally finite mass, which represent the Chern classes of the vector bundle.

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